X=3x+2x(7+4x)

Solution for X=3x+2x(7+4x) equation:

X=3X+2X(7+4X)

We move all terms to the left:

X-(3X+2X(7+4X))=0

We add all the numbers together, and all the variables

X-(3X+2X(4X+7))=0


We calculate terms in parentheses: -(3X+2X(4X+7)), so:

3X+2X(4X+7)

We multiply parentheses

8X^2+3X+14X

We add all the numbers together, and all the variables

8X^2+17X

Back to the equation:

-(8X^2+17X)


We get rid of parentheses

-8X^2+X-17X=0

We add all the numbers together, and all the variables

-8X^2-16X=0

a = -8; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-8)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-8}=\frac{0}{-16}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-8}=\frac{32}{-16}
=-2
$